GRAM: A framework for geodesic registration on anatomical manifolds

Medical image registration is a challenging problem, especially when there is large anatomical variation in the anatomies. Geodesic registration methods have been proposed to solve the large deformation registration problem. However, analytically defined geodesic paths may not coincide with biologically plausible paths of registration, since the manifold of diffeomorphisms is immensely broader than the manifold spanned by diffeomorphisms between real anatomies. In this paper, we propose a novel framework for large deformation registration using the learned manifold of anatomical variation in the data. In this framework, a large deformation between two images is decomposed into a series of small deformations along the shortest path on an empirical manifold that represents anatomical variation. Using a manifold learning technique, the major variation of the data can be visualized by a low-dimensional embedding, and the optimal group template is chosen as the geodesic mean on the manifold. We demonstrate the advantages of the proposed framework over direct registration with both simulated and real databases of brain images.